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arXiv · 1911.05593

Conservative, Dissipative and Super-diffusive Behavior of a Particle Propelled in a Regular Flow

Gil Ariel·Jeremy Schiff
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Abstract

A recent model of Ariel et al. [1] for explaining the observation of L\'evy walks in swarming bacteria suggests that self-propelled, elongated particles in a periodic array of regular vortices perform a super-diffusion that is consistent with L\'evy walks. The equations of motion, which are reversible in time but not volume preserving, demonstrate a new route to L'evy walking in chaotic systems. Here, the dynamics of the model is studied both analytically and numerically. It is shown that the apparent super-diffusion is due to "sticking" of trajectories to elliptic islands, regions of quasi-periodic orbits reminiscent of those seen in conservative systems. However, for certain parameter values, these islands coexist with asymptotically stable periodic trajectories, causing dissipative behavior on very long time scales.

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Gil Ariel, Jeremy Schiff. 2019-11-13. Conservative, Dissipative and Super-diffusive Behavior of a Particle Propelled in a Regular Flow. https://doi.org/10.1016/j.physd.2020.132584

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